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I thought I understood the "present value" of a series of cash flows but, I guess I don't.

As part of my financial plan, I want to calculate the present value of the income that my wife and I receive from our pensions and from our social security (and use the resulting numbers in our allocation planning).

I thought that present value gave me a number (X) such that, if I had X dollars invested at the specified rate, that the earnings from that investment would be equal to the income that the calculation is based on. However, when I calculate the present value using Excel's PV function, I don't get that. Here's an example:

Lets say I have a pension that's giving me $500 a month. Using an interest rate of 5% per annum and a 20 year time span, the formula would be: PV(5%/12 , 20 * 12, $500) = $75,763

However, $75,763 returning 5% per year generates only $315.68 per month.

What am I doing wrong here?

Is "present value" even what I want to be calculating here?

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I suspect the calculation presumes that as in a mortgage, your $500 per mo is composed of $315.68 in interest, plus a portion of the principle such that the account balance is zero after 20 years of payments.

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Apparently, what I want is not the "present value" calculation at all then.

If I do this instead: $500 / (5%/12) = $120,000.

IOW, $120,000 invested at 5% per annum would generate $500 per month. So, for planning purposes, that $500 a month pension would be the equivalent of $120,000 in CDs, right?

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I am no expert on present value, but no, I would not call the present value of $500/mo to be $120K. The $120K would still be there at the end of the payment period. You would get substantially more then that $500/mo from an annuity which assumes the $120K is depleted during the payment period.

To me, the present value is the cost of a 5% annuity that would pay $500/mo for 20 years.

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You are correct. And it's my thinking that I therefore do not want to use "present value" in my planning.

The way I see it, the $120,000 is the correct figure because it will never be depleted. I'm going to receive that pension check every month for the rest of my life. Just like if I was receiving $500 of interest every month from a $120,000 CD paying 5%. If I owned a $120,000 CD then, the day I die, it would still be worth $120,000.

So, for my planning purposes, that $500 a month coming in counts the same as having $120,000 in "fixed" assets.

If I'm incorrect in this line of thinking, I would appreciate someone straightening me out.

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**The way I see it, the $120,000 is the correct figure because it will never be depleted.**

You've discovered the key to 'old-money' wealth. Start with a huge pile of money, live off the interest and NEVER TOUCH the principal.

Most of us can't retire that way.

---------------------

Your pension models best as an annuity. At the end of 20 years, there's no principal remaining...

http://www.investopedia.com/calculator/AnnuityPV.aspx

Use 0.4166%, 240 months, 500 per month

Here's the way to model your scenario:

If you had $75,767.73 in an annuity at 5% annual interest, it would pay 500 per month for 20 years, then be empty.

That means: If you gave ME the money, I'd be able to pay you $6,000 the first year and invest the other $69,767.73 for a year at 5% interest. At the end of the year, I'd have $73,256.12 left. I pay you $6,000, then re-invest the remaining $67,256 for a year. In year 3, I have $70,618.80, pay you $6,000, invest $64,618. Each year, the principal is shrinking, but it will still last 20 years of fixed payments.

If, at the same time, you hide $44,244.39 in an account (a CD or similar) earning 5% interest (compounded monthly), at the end of 20 years, it would be worth $120,000.

http://www.investopedia.com/calculator/PVCal.aspx

This time, use 0.4166%/month for 240 months with a $120,000 final value.

Rick

No. of Recommendations: 1

DoLoop

The confusing point in calculating the present value of an annuity (a stream of payments) is that all you're calculating is the lump sum equivalent of the payment stream. That is, you're going from one form to another...the future value of both will be identical.

So in your case, the present value of a stream of payments at a fixed rate of return would have the following variables:

PV = $75,762.66

I = 5/12 = .4167%

N = 20*12 = 240 months

PMT = 500/mo

FV = 0

Its the FV = 0 that gets most students I teach. But its fixed at 0 so that you can find the equivalent of the two forms of payments....either a lump sum held for 20 years at 5%, or a stream of monthly payments over the same 20 year period at 5%: the two forms are saying exactly the same thing. To test this, calculate the FV of $500/mo at 5% or the FV of a lump sum of $75,762.66 invested at 5%. If you do the calculations, the future value in both cases will be $205,516.83.

BTW, this is how state lotteries work.

BruceM

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My take:

500 per month or 6000 per year income and 5% return is equilivent to starting with 76643 at the beginning of year 1, taking out 6000 per year, and the remaining capital earning 5% per year. At the end of 20 years you will have taken out 120000 and be left with zero capital.calculation.

simple excel spreadsheet

year start ...end ...out ..income

01 76643 74325 6000 3682

02 74325 71891 6000 3566

03 71891 69336 6000 3445

04 69336 66652 6000 3317

05 66652 63835 6000 3183

06 63835 60877 6000 3042

07 60877 57770 6000 2894

08 57770 54509 6000 2739

09 54509 51084 6000 2575

10 51084 47489 6000 2404

11 47489 43713 6000 2224

12 43713 39749 6000 2036

13 39749 35586 6000 1837

14 35586 31216 6000 1629

15 31216 26626 6000 1411

16 26626 21808 6000 1181

17 21808 16748 6000 940

18 16748 11435 6000 687

19 11435 5857. 6000 422

20 5857. 0.0000 6000 143

total withdrawal 120000

start = beginning of year balance

end = end of year balance

out = amount withdrawn per year

income = earnings at 5% of the average balance during year

No. of Recommendations: 1

*Lets say I have a pension that's giving me $500 a month. Using an interest rate of 5% per annum and a 20 year time span, the formula would be: PV(5%/12 , 20 * 12, $500) = $75,763*

However, $75,763 returning 5% per year generates only $315.68 per month.

What am I doing wrong here?

Nothing.

If you take 75,763 and get 5% per year interest, you can withdraw $500 per month for 20 years. At the end of 20 years, everything will be gone.

The difference between the 315.68 per month (in the first month) and the $500 you wish to draw is a return of your principal.

Instead, if you want to just get $500 a month and never touch the principal, all you need is to muliply by 12 (to get the annual amount), then divide by the interest rate (5% in your assumption) to get the principal you need - $120,000 as has been pointed out. In this case, at the end of 20 years, you will still have the $120k of principal. You've never touched it.

The difficulty in modeling a pension that you receive for life is that it involves some guesswork about the number of years you will receive it. You can look up life expectancy tables and get an average remaining life span if you'd like. I'm sure Google will find one for you. You could tweak one of those by thinking about your personal situation - your health and family history - adjusting the life expectancy up or down as appropriate.

Personally, I'd go the second route - making a personalized life expectancy guess. And you'll probably want to update this estimate periodcially - every couple of years or so.

An alternative approach to these benefits is to attack the problem from the spending side. Decide how much you want to spend in retirement. From that number, subtract off the pension income. The remainder of your spending will need to come from your personal savings. And in thinking about how much to keep in fixed income investments, you can use the lower spending figure as a basis for your calculations.

--Peter

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Rick, BruceM & gougmonk2 (Peter - see below)

I don't disagree with any of you. The calculations you've shown are absolutely correct. But what I can't get through my head is: which value is the "right" one to use for making asset allocation decisions?

Using the $500 a month example, the "present value" is $75,762.22 using a 20-year time frame. Calculating it "my" way, the value is $120,000 (with no time frame involved).

So, lets say that common wisdom dictates that I should have 40% of my investable assets in fixed income securities and 60% "in the market" (just for calculation purposes). Lets further assume that I have $500,000 in investable assets. I can come up *five* different allocations:

1) Totally ignore the pension and SS income:

Fixed: $200,000

Market: $300,000

2) Use the "present value" of the pension income:

- Add the present value to the investable assets, then split the total 40/60

Fixed: $230,304.88

Market: $345,457.34

- Split the investable assets 40/60, then consider the present value to be part of the 40% and take the rest from the investable assets. Put the balance of investable assets in the market

Fixed - present value: $75,762.22

Fixed - investable assets: $124,237.78

Market: $375,762.22

3) Same as #2 but use "my way" instead of present value:

- Add the "my way" value to the investable assets, then split the total 40/60

Fixed: $248,000

Market: $372,000

- Split the investable assets 40/60, then consider the "my way" value to be part of the 40% and take the rest from the investable assets. Put the balance of investable assets in the market

Fixed - "my way" value: $120,000

Fixed - investable assets: $80,000

Market: $420,000

Using the above different scenarios, I can "justify" putting anywhere from $300,000 to $420,00 into the market.

Which way is correct?

Peter -

Your response was posted while I was creating this reply. I like that alternative way of looking at it (noted in your last paragraph). I'm going to give that some serious consideration.

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*Using the above different scenarios, I can "justify" putting anywhere from $300,000 to $420,00 into the market.*

Which way is correct?

This isn't grade school where the answers are in the back of the book. There is no right or wrong answer.

The best we can say is that a reasonable allocation would fall somewhere between your two extremes.

What you actually do will depend not only on some basic formulas (which you really *do* seem to have a grasp of) but on human nature. What are you comfortable doing? When you think about a particular allocation how do you feel? You'll need to temper the results from any formula with what will let you sleep at night.

Asset allocation in retirement is not a science, it is an art.

--Peter

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*Personally, I'd go the second route - making a personalized life expectancy guess. And you'll probably want to update this estimate periodcially - every couple of years or so. *

Great advice from Peter. FWIW, I used the actuarial tables, did my plan and showed it to my wife. She actually took a quick look and punched me in the shoulder (she was a little angry), asking if I understood that her favorite Grandmother lived until 102, and I had a Grandfather who lived to be 92. Not good to deal with the consequences of averages there (it hurts in more ways than one). I revised the plan and did much of what Peter suggests.

Hockeypop

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Hockeypop

Further to Peter's excellent post, it depends on risk tolerance. Fixed income, say a ladder of CDs, will allow you to sleep at night but you and your long lived wife will probably dine less on steak and champagne then on hamburger and beer. Investing in the market and achieving the long term return of about 10% will supply a larger income stream but with some corresponding sleepless nights, particularly in a down market.

I would suggest 1) using the average life expectancy tables and adding a few years to the result, the number depending on health, life style and family history. Also, 2) consider that income needs will decrease with time. At 60 one may be traveling and golfing, at 80 exercise and daily excitement might be searching for the teeth each morning. One can start out with a larger income requirement than in the final years, seems I have read this somewhere but do not recall the source. The big expense in late life is the final hospitalization. Grim thought but that's life.

Use a spreadsheet to try different scenarios of life span for you and your wife, investment returns and income needs. Adjust every couple years as your situation changes and you develop a feel for your risk tolerance.

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*2) consider that income needs will decrease with time. At 60 one may be traveling and golfing, at 80 exercise and daily excitement might be searching for the teeth each morning. One can start out with a larger income requirement than in the final years, seems I have read this somewhere but do not recall the source. The big expense in late life is the final hospitalization. Grim thought but that's life. *

Good points with some concern by me over #2. I tested my suppositions about lower expenses over at the Rule Your Retirement site, and most of those folks advised not revising expenses down (which IS against conventional wisdom).

I think they would say that unless you're going to do less,the office expenses are made up for by vacation and other expenses (I certainly know in our case we plan vacations around business trips that help lower those costs). After a certain age many are also planning for significantly higher healthcare expenses.

Again, as you say, it's a combination of risk tolerance (and I've got in the habit of saving now so it doesn't "hurt" so bad). I do like Intercst's approach of reasonable "worst case" scenarios.

Thanks!

Hockeypop

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DoLoop after scanning all the replies I am not sure you got the answer -

There are some pretty common engineering calculations that deal with these issues.

http://www.investopedia.com/calculator/AnnuityPV.aspx

This link lets you enter your interest rate, years and amount. The correct answer is $75,763.16

One of the reasons you may not have gotten good answers are:

You need to use the interest rate per period -- so 5% per year is 0.41666% per month (the compounding period can make a small difference here)

Comments:

Most people would view an annunity, social security payments or a traditional pension payment as "part" of their fixed income portfolio.

Keep in mind if you want to have $500 per month of purchasing power for 20 years, you will need a great deal more dollars in 2025 then $500 -- While I do expect inflation, I would not project 5% annually. Even with the high inflation of the 70s, we still only have averaged 3% over the last 70 years.

Gordon

Atlanta

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Gordon said: *Most people would view an annunity, social security payments or a traditional pension payment as "part" of their fixed income portfolio. *

Thanks. I'm think I have a correct understanding of the various calculations. As Peter pointed out, I need to make up my own mind as to how to actually use these various numbers.

That led me to wonder just how "most" people or perhaps professional planners would do it. You addressed this question before I even asked it!

If I consider my pensions (I'm "retired" from 3 different companies), my wife's pension, my SS and my wife's SS, then, by even the most conservative of the calculations, I have adequate fixed income and should therefore put all of my investable assets in to the market.

I'm not quite sure yet if that approach would also satisfy the "sleep factor" - I'll have to think further about that. But it seems that I "should" put at least 80-90% in the market.

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How a 'real' financial planner would approach your investment and income needs issue will vary a bit between advisors, but I can outline what the CFP Board requires of its certificant's. (the 6-step process)

1. Determine client's needs and agree on scope of service

2. Gather data and reassess goals

3. Analyze data

4. Make recommendations

5. Implement per agreement

6. Periodically review

So, assuming your goal is to sustain your lifestyle at such-n-such a level over your projection of X years of life expectancy, and you provide documents that show what your current investable retirement holdings are and expected SS retirement benefits from your most recent statement, then the certificant should do the following, assuming other common needs have been met (risk managment, estate planning, emergency reserve, etc)

- determine the household income need from your investments, with the right mix of tax deferred and taxable account withdrawals

- determine the portfolio return you'll need to meet this.

- Asset allocate to meet this expected return

Now, of course, if the required rate of retun is outside of either reasonable market expectations or greater than your risk tolerance, then other alternatives would have to be employed, such as adjustments to household income and/or annual inflation adjustments, continue working years/defer starting SS, or other steps.

This is very general, but it is the approach that should be used. Notice, that it starts with needs/goal determination....not with how to invest...that comes last.

BruceM

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I am not a financial planner, but I have a broad financial and technical background. (The math does not bother me.) To me the purposes of 'fixed' income in a retirement vary -- it will not keep up with inflation. It does make sleeping easier in bear markets. The income puts a floor on the financial plan. When facing say 30 years of retirement even 2.5% inflation will decrease the purchasing value of $1,000 to $467.88 - so there is a need for equities unless a person has a whole lot of money.

My "test" for retirement is simple. Can you live next year on 4.00% of the money you have -- So I take my "expenses", subtract pensions and social security. Then if 4.00% of my IRAs plus other investments equals my "expenses" I am OK.

But to "stay" OK for 30 years I need to find a way to make that money grow even when I am unable to manage it - a stroke can change my abilities in 60 minutes. Frankly this is much harder then getting the money accumulated for me. There are lots of financial planners who will be happy to "help" me for one or two percent. But if that is true, then I am needed almost twice as much money for retirement.

I have been looking at this for a few years and now am finally comfortable with a plan. This plan undoubtedly will not work for many people, but it fits my needs.

Good luck

Gordon

Atlanta

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Bruce M:

"1. Determine client's needs and agree on scope of service

2. Gather data and reassess goals

3. Analyze data

4. Make recommendations

5. Implement per agreement

6. Periodically review"

That we agree upon.

"So, assuming your goal is to sustain your lifestyle at such-n-such a level over your projection of X years of life expectancy, and you provide documents that show what your current investable retirement holdings are and expected SS retirement benefits from your most recent statement, then the certificant should do the following, assuming other common needs have been met (risk managment, estate planning, emergency reserve, etc)"

That is where you really need to look at 'your lifestyle' and see if that is realistic, or if you want to change your lifestyle in retirement (ie, get the heck out of high price CA, NY state, or whereevr and move elsewhere).

Most people don't have realistic clue to needs other than the very tired "You need 80% of pre-retirement income" blah blah type stuff, with disregard to how much you are actually spending, saving, using for kids college, etc.

"- determine the household income need from your investments, with the right mix of tax deferred and taxable account withdrawals"

That is also a mistake that can lead you to woefully bad investment decisions.

The 'rule of thumb of 11% return on stocks' and similar is a recipe for distaster. the right mix of tax deferred and taxable account?? how about Ibonds and tax free munis and other things?

"- determine the portfolio return you'll need to meet this.

- Asset allocate to meet this expected return"

That can lead you down a road trying to get too much return on your nest egg, sssuming 11% growth in equities, not knowing what tax laws on cap gains, etc, will be.

To many think 5 or 6^ annual withdrawals are OK...

In one sense, if the persons goals are unrealistic, that should be worked on first (using a rough cut 4% withdrawal, plus other income like pensions, trusts, SS income, etc).......

Not you need $150,000 a year, how we going to fund that from your nest egg?......

And the other thing that is critically important is how much of a cut is the planner going to get from your 'investments' with him/her????? being a sucker for a salesman selling variable annuietes, or 'wraps' or insurance based insturments, or high load up front funds, isn't going to get you in good financial shape.....

t.

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*Using the above different scenarios, I can "justify" putting anywhere from $300,000 to $420,00 into the market.*

Which way is correct?

I don't know which way is "text-book" correct, or even which way a financial planner (highly overrated advice IMHO) would do it, but in real life I am using the "my way" method.

There is an implicit assumption in all of the present value calculations that money will have a worth after the time period under consideration. With retirement calculations, after a long enough time, I will be dead, and money will have no worth to me.

A fixed stream of income, from either a pension, SS, or any other source is exactly the same as a fixed-income investment to me if I am going to die. The way to handle inflation is to count the income stream as a fixed income investment and to adjust the equity/fixed **amounts** periodically to keep the ratio where you want it over time.

In our case, our fixed income streams are high enough to push 100% of our investable assets into equities and real estate. I am quite comfortable with this.